Finite Element Methods and Domain Decomposition

Language of Instruction

English

Pre-requirements

None

Learning Outcomes

After completing the course, students will be able to:

• Formulate typical boundary value problems for elliptic equations in variational form that satisfies the conditions of the Lax-Milgram theorem.
• Discretize boundary value problems using the Galerkin approximation with the classic finite element methods.
• Develop simple programs in MATLAB to form systems of linear equations that approximates elliptic equations with finite element methods.
• Apply the theory of Hilbert spaces and polynomial approximation to prove the convergence of the finite element method.
• Use the multigrid method domain decomposition techniques for solving large systems of linear equations.

Contact Information

advice@math.uib.no

Course offered (semester)

Autumn.

Language of Instruction

English

Aim and Content

The course considers the theory for finite element method to discrete partial differential equations, especially elliptical, and also solution techniques for the discrete equation system that become result. Domain decomposition as solving technique will become subject to special attention.

Learning Outcomes

After completing the course, students will be able to:

• Formulate typical boundary value problems for elliptic equations in variational form that satisfies the conditions of the Lax-Milgram theorem.
• Discretize boundary value problems using the Galerkin approximation with the classic finite element methods.
• Develop simple programs in MATLAB to form systems of linear equations that approximates elliptic equations with finite element methods.
• Apply the theory of Hilbert spaces and polynomial approximation to prove the convergence of the finite element method.
• Use the multigrid method domain decomposition techniques for solving large systems of linear equations.

Pre-requirements

None

Recommended previous knowledge

MAT260 Scientific Computing 2 and MAT232 Functional Analysis

Assessment methods

Written exam. If less than 20 students are taking the course, the exam may change to an oral examination.

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.

Contact Information

advice@math.uib.no